A Bayesian network is a probabilistic graphical model that aims to model conditional dependence (causation) among variables. In most cases, the true underlying structure of a set of variables is unknown. The number of possible structures grows explosively when we have more variables in the networks. Recovering the structure from a given data set is challenging. Many existing algorithms can learn structures from data automatically, but those algorithms may not be able to handle networks with hundreds or thousands of nodes. The focus is a score-based approach. However, sampling the partial order from a graph using MCMC methods requires intensive computational time, and the sampling scheme is biased. We develop a new MCMC sampling scheme for structural learning. The proposed sampling schem...[ Read more ]

A Bayesian network is a probabilistic graphical model that aims to model conditional dependence (causation) among variables. In most cases, the true underlying structure of a set of variables is unknown. The number of possible structures grows explosively when we have more variables in the networks. Recovering the structure from a given data set is challenging. Many existing algorithms can learn structures from data automatically, but those algorithms may not be able to handle networks with hundreds or thousands of nodes. The focus is a score-based approach. However, sampling the partial order from a graph using MCMC methods requires intensive computational time, and the sampling scheme is biased. We develop a new MCMC sampling scheme for structural learning. The proposed sampling scheme can potentially handle the problem of biasedness in existing methods. We demonstrate in simulations that our proposed method is more efficient to allow the graph samples to enter high score areas. We also illustrate our sampling scheme in a social science research study.